In deriving Bernoulli's equation , we equated the work done on the fluid in the tube to its change in the potential and kinetic energy. (a) What is the largest average velocity of blood flow in an artery of diameter `2xx10^(-3)m` if the flow must remain laminar ? (b) Do the dissipative force become more important as the fluid velocity increases ? Discuss quanlitatively .

Explanation

Diameter of artery `d=2xx10^(-3)m`
The coefficient of viscosity of blood `eta=2.084xx10^(-3)`PaS
Density of blood `rho=1.06xx10^(3)kg//m^(3)`
suppose , Reynold.s number for linear flow ,
`R_(e)=2000`
Maximum average velocity of blood,
`v_("avg")=(R_(e)eta)/(rhoD)=(2000xx2.084)/(1.06xx10^(3)xx4xx10^(-3))`
`=0.98m//s`
(b) Volume of fluid passing per second, `Q=av_("arg")`
`=(pi^(r2))v_("avg")`
`=(22)/(7)xx(2xx10^(-3))^(2)xx0.98`
`=1.23xx10^(-5)m^(3)s^(-1)`
As per fluid velocity increases , the dissipative forces become more important . This is because of the rise of turbulence . Turbulent flow causes dissipative loss in a fluid.